Question

Which of the following properties can be used to show that the expression 4^5/3 is equivalent to ^3√4^5

Answer 1

Answer:

$\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5}{3}}$

Option 1 and Option 3 is correct

Step-by-step explanation:

Given: $4^{\frac{5}{3}}=\sqrt[3]{4^5}$

This is exponent to radical change property.

The fraction exponent write as radical.

$a^{\frac{m}{n}}=\sqrt[n]{a^m}$

• Option 1:  Radical to exponent

$\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5}{3}}$

True

• Option 2: Addition of exponent if base is same.

$4^{\frac{8}{3}}\cdot 4^{\frac{7}{3}}=4^{{\frac{8}{3}+\frac{7}{3}}=4^5$

False

• Option 3: Multiply exponent to exponent, True
• Option 4: Division property of exponent, False

Answer 2

Answer: First option.

Step-by-step explanation:

For this exercise it is importnatn to to remember the properties that are shown below:

1) $a^\frac{1}{n}=\sqrt[n]{a}$

2) $(a^m)^n=a^{(mn)}$

Therefore, given the following expression provided in the exercise:

$\sqrt[3]{4^5}$

You can apply the properties mentioned before, in order to find an equivalent expression.

Therefore, you get:

$\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5*1}{3}}=4^{\frac{5}{3}}$

Then the answer is the first option.